SUR LES FEUILLETAGES TRANSVERSALEMENT HOMOGÈNES A SOUS-GROUPE DISCRET.
Résumé
G{Γ} being the group generated by left translation of a Lie group G and right translation of elements of a discrete subgroup Γ, we establish here that on a manifold M, there is a correspondance one to one between (G/Γ)- homogenous transversally foliations and foliations given by a (G{Γ} ,G)- transverse structure, and two corresponding foliations have the same C^{∞}-transverse structure. Moreover one foliation of (G{Γ} ,G)- transverse structure is a Lie foliation if and only if its Γ-holonomy group is trivial.
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